Hello Santosh Katke,
The LPC1768 RTC don't work reliably problem seems the existing problem, because I have found it in the LPC176X errata.
http://www.nxp.com/docs/en/errata/ES_LPC176X.pdf

Still no work-around.
But you said the external crystal stops oscillating, I think it also relate to the external crystal hardware, you may try to change the load capacitor, and test it again.
Have a great day,
Kerry
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